What I don't get about the 'influence' and 'changes position' argument is that - so many times we have seen a guy be a meter offside and jump over a ball to leave it for a runner coming from a non-offisde position. I have a few instances in my mind but am unable to recollect the exact game/goal, but you guys surely know what I'm talking about - defenders scramble to mark a guy who is clearly offisde but he either jumps over the ball or just moves aside. In this case, the defenders are CLEARLY affected as they weren't expecting someone from the back to run on to the ball.
If that is not called offside, then why is this being called offside? Either they should both be off, or both be on. Right now it's arbitrary and makes no sense.